Post acquisition image processing is well known in the literature. Publications which describe the general state of the art in post acquisition image processing are: Lim, J. S. “Two dimensional signal and image processing”. Englewood Cliffs, N.J. Prentice Hall. (1990); Russ, J. C. “Image processing handbook”. CRC Press. (1992); Pratt, W. K. “Digital image processing”. NY John Wiley & Sons, Inc. (1991); Rosenfeld, A. and Kak, A. C. “Digital picture processing”. Academic Press. (1976); Castleman, K. R. “Digital Image Processing”. Prentice-Hall Inc. Englewood Cliffs, N.J. (1979).
Imaging which provides information relating to refractive characteristics in a imaged volume is known for extremely limited applications. In microscopy, Smith, Nomarski and Differential Interference Contrast (DIC) imaging is known and is described in the following publications: Nomarski, G. “Microinterferometer differential a ondes polarisees”. J. Phys. Radium 16:9S–11S (1955); Lang, W. “Differential-Interferenz-Miikroskopie”. Carl-Zeiss, Oberkochen (1975); Inoui, S. and Spring, K. S. “Video Microscopy: the fundamentals”. 2nd edition. Plenum Press, NY. (1997). Tanford, C. “Physical chemistry of macromolecules”. John Wiley NY. (1961). Appendix C describes classical Rayleigh interference methods, Philpot and Svenson methods based on schlieren image, Lamm method of line displacement, and Gouy interference method all developed for determination of one dimensional refractive index variations.
Computer analysis of DIC imaging is not readily achieved. Known instances are described in the following publications: Allen, R. D., Allen, N. S. and Travis, J. L. “Video-enhanced contrast, differential interference contrast (AVEC-DIC) microscopy: a new method capable of analyzing microtubule related motility in the reticulopodial network of Allogromia laticollaria.” Cell Motility 1: 291–302 (1981); Cogswell, C. J. and Sheppard, C. J. R. “Confocal differential interference contrast (DIC) microscopy: including a theoretical analysis of conventional and confocal DIC imaging”. J. Microsc. 165:81–101 (1992); Gelles, J., Schnapp, B. J. and Sheetz, M. P. “Tracking kinesin-driven movements with nanometer-scale precision”, Nature 331:450–453 (1988); Hdusler, G. and Kvrner, E. “Imaging with expanded depth of focus”. Zeiss Inform. 29: 9–13 (1987); Preza, C., Snyder, D. L. and Conchello, J-A. “Image reconstruction for three-dimensional transmitted light DIC microscopy”. SPIE 2984:220–231 (1997); Schormann, T. and Jovin, T. M. “Contrast enhancement and depth perception in three-dimensional representations of differential interference contrast and confocal scanning laser microscope images”. J. Microsc. 166:155–168 (1992).
Computerized ray tracing between discrete refractive and reflective surfaces is extremely well developed, but is not well known in the environment of non-homogeneous indices of refraction. This area is described in the following publications: Hecht E. and Zajac A. “Optics” 2nd ed. Addison-Wesley Reading Mass. (1997); Jenkins, F. A, and White, H. E. “Fundamentals of optics”. McGraw-Hill, NY (1950) ch. 8: Ray Tracing.
Calculation of point spread functions (PSF) is extremely well known as described in the following publication: Born M. and Wolf E. “Principles of Optics” Pergamon London (1959); Goodman J. W. “Statistical Optics” John Wiley & Sons NY (1985); Hecht E. and Zajac A. “Optics” 2nd ed. Addison-Wesley Reading Mass. (1997); Gibson S. F. and Lanni F. “Diffraction by circular aperture as a model for three-dimensional optical microscopy”. Opt. Soc. Am. A 6:1357–1367 (1989); Gibson S. F. and Lanni F. “Modeling aberrations due to mismatched layers for 3-D microscopy” SPIE optics in complex systems 1319:470–471 (1990); Gibson S. F. and Lanni F. “Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy”. J. Opt. Soc. Am. A 8:1601–1613 (1991).
Deconvolution of three dimensional microscopic images having location independent PSF is well known and is described in the following publications, some of them authored by some of the present inventors: Jansson, P. A. ed. “Deconvolution of images and spectra”. Academic Press NY (1997); Agard, D. A. and Sedat, J. W. “Three-dimensional architecture of a polytene nucleus”. Nature 302:676–681 (1984); Agard, D. A., Hiraoka, Y., Shaw, P. and Sedat, J. W. “Fluorescence microscopy in three dimensions”. Methods in Cell Biology 30: 353–377 (1989); Castleman, KR. “Digital Image Processing”. Prentice-Hall Inc. Englewood Cliffs, N.J. (1979). Correction of telescopic images by the use of suitably distorted mirrors and deconvolution of two dimensional telescope images having location dependent PSF are described in the following publications: Boden, A. F., Reeding, D. C, Hanisch, R. J., Mo, J. and White, R. “Comparative results with massively parallel spatially-variant maximum likelihood image restoration”. Bul Am Astr. Soc 27:924–929 (1995); Boden, A. F., Reeding, D. C, Hanisch, R. J. and Mo, J. “Massively parallel spatially-variant maximum likelihood restoration of Hubble space telescope imagery”. J Opt Soc Am A 13: 1537–1545 (1996); Jansson, P. A. ed. “Deconvolution of images and spectra”. Academic Press NY (1997), Tyson R. K. “Principles of Adaptive Optics” Academic Press NY (1991). Reconstruction of blurred images from point objects is described in the following publications: Carrington, W. A., Lynch, R. M., Moore, D. W., Isenberg, G., Fogarty, K. E. and Fay, F. S. “Superresolution three-dimensional images of fluorescence in cells with minimal light exposure”. Science 268:1483–1487 (1995), Femino, A. M., Fay, F. S., Fogarty, K., and Singer, R. H. “Visualization of single RNA transcripts in situ”. Science 280:585–590 (1998).